On Representatives of Subsets

Hall, P. (1935). On Representatives of Subsets. Journal of the London Mathematical Society, 26-30.

Type

Journal article

Intellectual base

Primary research

Year

1935

Pages

26-30

DOI

10.1112/jlms/s1-10.37.26

DOI registrant

Wiley

Link

https://doi.org/10.1112/jlms/s1-10.37.26

Cited by

2 citations across 2 artifacts.

Domain-specific

• Matching
  • Hall's marriage theorem (1935) characterizes when a bipartite graph has a matching saturating one side: a bipartite graph with sides \(A\) and \(B\) has a matching saturating \(A\) if and only if every subset \(S \subseteq A\) has at least \(|S|\) neighbors in \(B\) — the marriage condition

    SupportedVerified against the source

    Read by an automated reader; not a human review. How support was checked

• Transversal (Combinatorics)
  • In combinatorics, a transversal or system of distinct representatives for an indexed family \(\mathcal F=(A_i)_{i\in I}\) is a choice function \(f:I\to\bigcup_i A_i\) such that \(f(i)\in A_i\) for every index and \(f\) is injective.

Verification

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Registry ID ref:1fcda08a4ea7 · see in the full table